Create Prime Number Set

[wdcraft01]

It would be useful to have a representation of the set of prime numbers. We have not engaged in much number-theoretic work in Prove-It, but the concept of prime numbers still occasionally arises. For example, sets of the form $\{0, 1, 2, \ldots, n-1\}$ under mod $n$ addition and multiplication are actually finite fields, but only when the order $n$ has the form $n = p^{k}$ for some prime $p$ and positive integer $k$.

There seems to be no widely agreed-upon notation to represent the set of primes. The Wikipedia entry on prime numbers notes that the set of all primes is sometimes denoted as P or ℙ (or an equivalent “math bubble font,” which doesn't work here in the GitHub Markdown) Wikipedia: Prime Number .

The most appropriate place for a prime number set seems to be in numbers/number_sets/integers, perhaps established as an extension of the IntegerSet (which is itself an extension of NumberSet). Consistent with the extant notation, it seems appropriate to call the class PrimeSet (analogous to IntegerSet, NaturalSet, ComplexSet, etc).